**What is eddy current?**

**eddy current loss.**

The eddy current loss can be minimized by use of thin laminated silicon steel sheets in place of solid steel sheet. The various factor like magnetic flux density, frequency, electrical properties of the material and thickness of the laminated sheets affect the eddy current loss. The **derivation of the eddy current loss formula** gives in-depth overview of the factors on which eddy current loss depends.The formula of the eddy current loss(P) is as given below.

Let us derive the formula of the eddy current loss for better understanding of the eddy current loss in a steel core.

**Derivation of eddy current loss formula**

_{max}Sinωt

Let us consider a small elemental closed loop path PQRSP of thickness d

*x*and distance of the small element from origin is

*x*. The voltage will be induced in this close loop similar to as induce in a single turn coil.

Area of the loop PQRS(A) = 2h

*x*——-(1)

*Theflux density B = Φ/A*

The flux crossing the loop PQRSP =

_{max}Sinωt2h

*x*——————-(2)

E=

**4.44**f

_{Φmax }

_{ }E=

**√**

**2Π**f Φmax [

**√**

**2Π=4.44]**

**E=**

**√**

**2 Π**f Bmax A

E= √2Π f B

_{max}

^{2 }h

*x*——————-(3)

Resistance of the eddy current path

R = ρ * ( 2h+4x)/ L d*x* ————–(4)

The eddy current loss(*d*P) in a small elemental loop d*x*

*d*P = E^{2}/R

*d*P = E^{2} Ld*x/*[ρ * ( 2h+4x)] ——–(5)

Since thickness of the sheet is very less compared to height of the sheet and *x* dimension can be ignored.

*d*P = E^{2} Ldx/(ρ*2h)

*d*P = [√2ΠfB_{max}2hx]^{2} Ldx/(ρ*2h)]

*d*P = [4ΠfB_{max}2hx]^{2} Ldx/(ρ*2h)]

*d*P = ^{4Π2Bmax2f2}^{hL/ρ ———-(6)}

Total eddy current loss =

The volume of sheet (V) =hL𝞃

Eddy current loss per unit volume =

_{eddy}=

*Π*𝞃

^{2}Bmax^{2}f^{2}^{2}

*/*

^{6ρ——–(7)}*P*

_{eddy}= K_{e }*f*

^{2 }*Bmax*𝞃

^{2}^{2 —————(8)}

^{Where,}

*K*Π

_{e = }^{2}/6

*ρ*

**is called the**

*K*_{e }**eddy current coefficient.**

**Thus the eddy current loss per unit volume is ;**

- Proportional to the square of the frequency
- Proportional to the square of the flux density
- Proportional to the square of the thickness of the laminated sheet
- Inversely proportional to the resistivity of the material

**How to minimize eddy current loss?**

^{2}R) reduce in the thin laminated sheet.

The other electrical quantity that affects the eddy current loss is the ratio of the voltage and frequency.The eddy current loss remains constant if the following electrical quantities remains constant.

- Voltage
- Frequency

**flux density will also remains constant**because the flux density is proportional to the ratio of V/f.

Applications of Eddy Current

The eddy current is undesired in the motor, transformer as it cause heat loss which is wastage of energy. However, the eddy current can be usefully used in the following applications.

**Damping:**The coil of the measuring instrument is mounted in the light metal frame. When the coil and the pointer rotate in the permanent magnetic field, the eddy current induces in the metal frame which produce the damping torque.

**Electric Brakes:**When a stationary magnetic field is applied to a rotating drum, the eddy current set up in the drum produce the braking torque. The brakes are known as eddy current brakes.

**Induction Furnace:**In induction furnace, the metal which is to be heated up is placed in the rapidly changing magnetic field produced by high frequency current. The eddy current is set up in the metal piece and thus the metal get heated up. The induction bearing heater also functions on the same principle.

- The effect of eddy current is used for providing braking torque in induction type energy meters.

- Eddy current instruments are used for detecting cracks in the metal parts.

**Related Posts**

Does this formula work if magnets slide down a single aluminium sheet, rather than an entire core of laminated sheets? Thanks!